On HL 2(L,L) for semisimple Leibniz algebras

Algebra, Analysis and Quantum Probability

Camacho, L.M.^1 ; Ladra, M.^2 ; Turdibaev, R.M.^1

Dpto. Matemática Aplicada I., University of Sevilla, 41012, Spain^1

Department of Algebra, University of Santiago de Compostela, 15782, Spain^2

关键词: Direct sum;    Finite dimensional;    Leibniz algebras;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/697/1/012008/pdf
DOI  :  10.1088/1742-6596/697/1/012008

来源: IOP

【 摘 要 】

In this paper we present a decomposition of HLn(L, L) into a direct sum of some subspaces for a finite dimensional complex semisimple Leibniz algebra L. Furthermore, we provide a more specific decomposition in case n = 2 into two subspaces. We verify that one of those subspaces annihilates for specific Leibniz algebras with liezation2and some others.